Calc 1

Consider the following function.
f(x) = x^6 ln x

(a) Use l'Hospital's Rule to determine the limit as x → 0+.

(b) Use calculus to find the minimum value.

Find the interval where the function is concave up. (Enter your answer in interval notation.)

Find the interval where the function is concave down. (Enter your answer in interval notation.)

  1. 👍 0
  2. 👎 0
  3. 👁 519
  1. basic stuff.

    f(x) = lnx/x^-6
    limit is same as (1/x)/-6x^-5 = -x^4/6 = 0

    f'(x) = x^6 * 1/x + 6x^5 lnx = x^5 (1+6lnx)
    so, f'=0 when x = e^(-1/6)

    f" = x^4 (11+30lnx)
    x^4 is always positive, so, f" > 0 when lnx > -11/30, or x > e^(-11/30)

    I expect you can rephrase that as an interval.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math Test

    1. A rental car company charges $150.00 for a weekly rental and an additional $0.20 for each mile driven. The function rule C=0.20m+150.00 describes the relationship between the number of miles driven m and the total cost C. If

  2. Math

    Write a function rule to represent the situation. The total cost C for g grams of buffalo meat if each gram costs $3.43 Write a function rule using C and G as variables

  3. Math

    1.Suppose that the function f(x) = 5x + 3 represents the number of cars that drive by in x minutes. How many cars will drive by in 10 minutes? a. 80 b. 53 c. 50 d. 35 2. Buses on your route runs every 8 minutes from 7:00am to

  4. Math help! Hurry Please~

    1. Scientists estimate the rate of the wildebeest running at full speed to be 66 feet per second. Write a function rule to describe the relationship between the time, t, and the distance ,d, a wildebeest travels when running at

  1. Pre-Algebra

    1. Given the function rule f(x) = x² – 3x + 2, what is the output of f(–2)? 2. Suppose you earn $12 each time you mow the lawn. Write the function describes the relationship between your total earnings E and the number of

  2. calculus

    Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→∞ {(5x − 4)/(5x + 3)}^5x + 1

  3. MATH

    15. Write a function rule that represents y is 5 less than the product of 4 and x. 16. Write a function rule that represents 7 less than three fifths of b is a. 17. Write a function rule that represents the almond extract a

  4. calculus

    Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→0 (e^x − e^−x − 2x)/(x − sin(x))

  1. Math I need help ASAP!

    1) Identify the function rule shown in the table. Function Table n - 3, 4, 5, 6 y - 2, 1, 0, -1 a. y = 2 + n b. y = 5n c. y = 5 - n d. not enough information ** 2) What is the values of the function y = -2x - 4 for x = 0,1,2 and

  2. Calc 1

    Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→∞ x^7e^−x^6 Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method,

  3. Math ~ Check Answers ~

    Explain how to write a function rule from the table below. Then write a function rule. X: 2 | 4| 6 | And: 1 | 0 | -1 | My Answer: y = -1/2 x But, -1/2 (2) = -1, and y(2) = 1, so we need to add 2 at the start. So, y = 2 - 1/2 x

  4. Algebra

    Create a function rule for the following: x 0 3 6 f(x) -5 -3 -1 How do I create a function rule? I forgot how to and nowhere online is giving me a good example of how to.

You can view more similar questions or ask a new question.